I don't understand the question, could you provide a reproducible example?
For example, if you have a vector x, you can get such a frequency table with cut() (to assign each observation to an interval), and table() (to count the number of observations in each interval:
# generate fake data
set.seed(1)
x <- round(113*runif(100))
# Cut into intervals and generate frequency table
table(cut(x, breaks = c(1,6,15,18,21,25,40,60,65,113)))
#>
#> (1,6] (6,15] (15,18] (18,21] (21,25] (25,40] (40,60] (60,65]
#> 2 8 1 2 4 14 23 2
#> (65,113]
#> 44
Created on 2022-05-23 by the reprex package (v2.0.1)
In your data, I'm not sure if you started from such a vector x, how the breakpoints were chosen, and how the "modified" frequency table was obtained from the first one.